Explanation

(d) Neutron velocity $= v$, mass $= m$
Deuteron contains 1 neutron and 1 proton, mass $= 2m$
In elastic collision both momentum and $K.E.$ are conserved $p_{i} = p_{f}$
$mv = m_{1}v_{1} + m_{2}v_{2} \Rightarrow mv = mv_{1} + 2mv_{2}$ …(i)
By conservation of kinetic energy
$\frac{1}{2}mv^{2} = \frac{1}{2}mv_{1}^{2} + \frac{1}{2}(2m)v_{2}^{2}$ …(ii)
By solving (i) and (ii), we get
$v_{1} = \frac{m_{1} - m_{2}}{m_{1} + m_{2}}v + \frac{2m_{2}}{(m_{1} + m_{2})}v \Rightarrow v_{1} = \frac{m_{1} + 2m}{3m} = - \frac{v}{3}$
$K_{i} = \frac{1}{2}mv^{2},\ K_{f} = \frac{1}{2}mv_{1}^{2} \Rightarrow \frac{K_{i} - K_{f}}{K_{i}} = 1 - \frac{v_{1}^{2}}{v^{2}}$
$= 1 - \frac{1}{9} = \frac{8}{9}$ [Fractional change in $K.E.$]